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A343681
Zuckerman numbers which when divided by product of their digits, give a quotient which is also a Zuckerman number.
3
1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 24, 36, 111, 128, 135, 144, 175, 384, 672, 735, 1111, 1296, 1575, 11111, 22176, 42624, 82944, 111111, 139968, 688128, 719712, 1111111, 1161216, 1492992, 2241792, 2794176, 4136832, 4741632, 6838272, 11111111, 12171264, 13395375, 13436928
OFFSET
1,2
COMMENTS
Alternative Name: Zuckerman numbers k such that k/(product of digits of k) is also a Zuckerman number. - Wesley Ivan Hurt, Apr 26 2021
All positive repunits are terms (A002275).
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..160 (terms < 3*10^14)
Giovanni Resta, Zuckerman numbers, Numbers Aplenty.
EXAMPLE
24 is a Zuckerman number as 24/(2*4) = 3, 3/3 = 1 so 3 is also a Zuckerman number, and 24 is a term.
1296 is a Zuckerman number as 1296/(1*2*9*6) = 12, 12/(1*2) = 4 so 12 is also a Zuckerman number and 1296 is a term.
MATHEMATICA
zuckQ[n_] := (prod = Times @@ IntegerDigits[n]) > 0 && Divisible[n, prod]; Select[Range[10^6], zuckQ[#] && zuckQ[#/Times @@ IntegerDigits[#]] &] (* Amiram Eldar, Apr 26 2021 *)
PROG
(PARI) isz(n) = my(p=vecprod(digits(n))); p && !(n % p); \\ A007602
isok(n) = isz(n) && isz(n/vecprod(digits(n))); \\ Michel Marcus, Apr 26 2021
CROSSREFS
Cf. A235507 (similar, with Niven numbers).
Sequence in context: A064700 A180484 A007602 * A337941 A167620 A169935
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Apr 26 2021
EXTENSIONS
More terms from David A. Corneth, Apr 26 2021
STATUS
approved